Kinesthetic Function Diagrams

I start by doing the “function diagram dance” for my students. (To understand this, you need to already be familiar with function diagrams.)

The idea of the dance is that my right hand represents x and my left hand represents y. (From the student’s perspective, this puts the x on the left and the y on the right, where they should be.) As I move my x hand from negative infinity (all the way down) to positive infinity (all the way up), I move my y hand in various ways, for example exactly along the x, for y=x, or consistently ahead of the x, for y=x+1, or twice as fast as the x for y=2x. Each time, the students have to figure out the function I am representing. (This only works for very simple functions, such as y=mx, or y=x+b.) After dancing some examples myself, I ask the students to do the dance, at first with functions similar to mine, then perhaps some new ones such as for example for y=-x and y=-2x.

I usually close the door right before doing this. This way they don’t have to worry about being seen.